# Trouble with tension

Two persons A & B are pulling the two ends of a rope (As people do in tug war).Person A pulls rope with a force=10N and the person B is pulling another end of the rope with a force =20N. According to Newton's 3rd, rope will also pull person A with force=10N and B with a force=20N. It means tension at one end of the rope is 10N and at the other end tension is 20N(Because of the definition of tension).Is it correct? If yes ,then pulling force on A by the rope will only depend on force exerted by A on rope and will not depend upon the force applied by B on the rope. In that case , if B is pulling the rope with a force=1000N and A is pulling the other end of rope with a force=10N, then the tension at that end(where A is applying force) will be only 10N.It means the force by which rope is pulling A will be only 10N. Is it possible?

• Related – Farcher Nov 26 '18 at 8:58
• Hi naveen. Please do not copy-paste the same comment to ping multiple people, especially if it is not directly related to anything they have said. – ACuriousMind Nov 26 '18 at 17:57

$$\def\qy#1#2{#1\,\mathrm{#2}}$$ Your trouble arises from an implied assumption: that ropes always transmit unchanged tension, or in other words that tension is the same in all points of a rope.

Actually this is true in one of these situations:

• rope's mass is negligible
• rope has no acceleration.

So it must be seen if one or the other is consistent with your data. You said nothing about rope's mass - let's take it of $$\qy1{kg}$$ (usually it will be lower). Net force on the rope is $$\qy{10}N$$, so rope's centre of mass will have an acceleration $$\qy{10}{m/s^2}$$.

It's obvious that such state of things can only last for a small fraction of a second. It will end when both persons do apply equal forces. Note that during acceleration tension along the rope is not uniform. You can convince of that by applying Newton's second law to any segment of rope. Its being accelerated requires different forces acting at its extremes.

If instead the rope's mass is really negligible, then your data are simply impossible: the two persons can't apply different forces to the rope.

No, the tension is equal across the whole rope but the forces that pull on each person (and effectively move the weaker person and the rope towards the stronger person) result fom adding the forces under consideration of the direction they are applied (i.e. one of them will have negative sign).

This information should be enough to figure out what the tension on the rope is if you think about in what situation all applied forces only act as tension and at what point part of the force will cause the movement.

" pulling force on A by the rope will only depend on force exerted by A on rope and will not depend upon the force applied by B on the rope."

In a manner of speaking, yes. But not the correct manner of speaking. The force of $$A$$ on the rope will always be equal to the force of the rope on $$A$$ regardless of what $$B$$ is doing. But that does not mean that both of those forces will not increase as $$B$$ pulls harder.

• if B pulls harder then the force of the rope on A increases, okey. But how will the force of A on the rope increase as B pulls harder? – naveen Nov 26 '18 at 12:00
• Well, that's Newton's Third Law. That's the way nature works. I think perhaps you are taking a view that's too "global". There's a force $A$ on rope, and a force rope on $A$. Think locally. That these forces are equal has nothing to do with anything else. Including whether or not the point of contact is in motion of any kind, or what's happening at the other end of the rope. – garyp Nov 26 '18 at 13:46
• i am still stressed but i will keep your idea in mind – naveen Nov 26 '18 at 16:20